Final answer:
Mary Rothbart's dimension of temperament related to the time children dedicate to a single task like a puzzle is called attention span/persistence. It's a measure of the ability to remain focused and is essential in understanding children's self-regulation.
Step-by-step explanation:
The dimension of temperament proposed by Mary Rothbart that captures the duration of time children can concentrate and work on a single task, such as a puzzle, is called attention span/persistence. This dimension is one of the several outlined by Rothbart to describe the various aspects of children's temperament. Attention span/persistence specifically measures a child's capacity to stay engaged with a task despite distractions and challenges. This aspect of temperament is critical in understanding how children regulate their behavior and emotions in response to different stimuli or tasks.